(2x-10)(5x+15)=0

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Solution for (2x-10)(5x+15)=0 equation:


Simplifying
(2x + -10)(5x + 15) = 0

Reorder the terms:
(-10 + 2x)(5x + 15) = 0

Reorder the terms:
(-10 + 2x)(15 + 5x) = 0

Multiply (-10 + 2x) * (15 + 5x)
(-10(15 + 5x) + 2x * (15 + 5x)) = 0
((15 * -10 + 5x * -10) + 2x * (15 + 5x)) = 0
((-150 + -50x) + 2x * (15 + 5x)) = 0
(-150 + -50x + (15 * 2x + 5x * 2x)) = 0
(-150 + -50x + (30x + 10x2)) = 0

Combine like terms: -50x + 30x = -20x
(-150 + -20x + 10x2) = 0

Solving
-150 + -20x + 10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '10'.
10(-15 + -2x + x2) = 0

Factor a trinomial.
10((-3 + -1x)(5 + -1x)) = 0

Ignore the factor 10.

Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-3, 5}

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